Topic selection is the first step of your math IA journey. A high-achieving math IA topic is unique, mathematically rigorous, and personally engaging. Most importantly, fully understanding the topic and executing the production of a well-written investigation should be manageable within the student’s academic aptitude. This is why the topic selection process can be troublesome for both students and teachers; finding the right topic that is just difficult enough to be intellectually stimulating, yet not too difficult to be beyond the student’s capabilities is an arduous drill that takes everyone involved on a roller coaster of emotions (e.g. excitement at the discovery of a topic, quickly followed by disappointment as one realizes one or more disqualifying factors for the topic). Teachers often reject a student's initial topic that does not fulfill the aforementioned criteria. Common reasons for topic rejection include:
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Overlapping topics with classmates
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cliché topics
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Overly difficult/ incomprehensible topics
If your topic is rejected, it is crucial to understand the specific reason. How can we lower the likelihood of a topic being rejected? And how can we wisely respond to topic rejection?
Overlapping topics with classmates
Your teacher may decline your topic if other classmates are already working on a similar topic. Some teachers may utilize a first come, first served policy when two students pitch similar research questions. Hence, you should start brainstorming as soon as possible and check with your teacher before writing the first draft to avoid overlapping with your classmates. Nevertheless, if your topic is rejected due to overlapping, you should try pivoting to a similar topic or you should quickly develop a new topic.
Cliché
Come on, we know everyone and their cousins did (Susceptible-Infected-Recovered) SIR epidemic modeling during the COVID years.
Are you sure you want a simple linear regression model to serve as the pinnacle highlight of your knowledge and understanding as an AA HL student?
A successful math IA topic should be distinctive and personal. In such cases, instead of starting from scratch, you should try to develop your original idea. For instance, the topic of the SIR model can be varied by adding more rigorous ideas, such as diffusion equation and graph theory, that have not been used in the past IAs. By pivoting to an adjacent topic of a higher difficulty, you can achieve a higher mark in Criterion E: Use of Mathematics and while still retaining your personal engagement story. You are always welcome to ask your school teacher and/or personal tutor for help in researching and understanding advanced mathematics that are slightly out of your league.
Overly difficult/ incomprehensible topics
(Are you sure you can solve the Navier-Stokes existence and smoothness problem? One of the seven millennium prize problems with a $1 million bounty on its head? Although a math IA should be academically challenging, it must be understandable to both the student and the examiner (a.k.a your teacher, as this is an internal assessment). If your teacher gets the impression that you do not comprehend your own topic and that your topic is unmanageable, they may decline your topic. Hence, you must do your due diligence in researching your topic to succinctly communicate your specific aim to your teacher and secure their support. Thoroughly prepare a written proposal and oral elevator pitch that includes your aim, action plan, structure, and use of mathematics. Your teacher wants you to succeed, so they will accept your topic only if they are convinced of your ability to accomplish the proposed aim and deliver results. If you think that your teacher is being too conservative, even underestimating your ability to take on a challenging topic, you can still push through with your topic to convince him otherwise. However, being confrontational or insubordinate is not recommended;as your teacher is the ultimate decision maker who grades your IA (don’t bite the hand that feeds you!). More often that not, the safe choice is to consider simplifying your topic to tone down the complexity/ difficulty of your topic.
As seen, topic selection is a highly delicate process that lays out the basis for a high-achieving math IA, and fulfilling all the required criteria for an outstanding topic may be extremely challenging for a student to accomplish independently. In such cases, you can receive external help from an experienced tutor. A veteran tutor will have experience successfully coaching numerous students to find the right IA topics tailored to a broad spectrum of interests and abilities.